GCF of 829/69, 266/12, 238/96
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 829/69, 266/12, 238/96 i.e 1/2208 easily. The following is the detailed procedure to determine the greatest common factor of fractions 829/69, 266/12, 238/96.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 829/69,266/12,238/96?
Given fractions are 829/69,266/12,238/96
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 829/69,266/12,238/96, numerators are 829,266,238
Denominators are 69,12,96
The GCF of 829,266,238 is 1 .
LCM of 69,12,96 is 2208.
The greatest common factor of 829/69,266/12,238/96 = [GCF of 829,266,238]/[LCM of 69,12,96]= 1/2208
Therefore, the GCF of 829/69,266/12,238/96 is 1/2208.
To find the highest common factor of 829,266,238, we have to find the factors of both numbers and list the highest common factor.
The factors of 829 are 1, 829
The factors of 266 are 1, 2, 7, 14, 19, 38, 133, 266
The factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238
The HCF of 829,266,238 is 1.
Lets's calculate GCF of 829,266,238
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 829,266,238 By Matching Biggest Common Factor Method
Now, list down the factors of 829
:1,829
Now, list down the factors of 266
:1,2,7,14,19,38,133,266
Now, list down the factors of 238
:1,2,7,14,17,34,119,238
Greatest Common Factor
We found the factors 829,266,238 . The biggest common factor number is the GCF number.
So the greatest common factor 829,266,238 is 1.
Lets's calculate LCM of 69,12,96
| 2 | 69, 12, 96 |
| 2 | 69, 6, 48 |
| 3 | 69, 3, 24 |
| 23, 1, 8 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 23 x 1 x 8 = 2208
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2208
Therefore, the GCF of Fractions 829/69,266/12,238/96 is 1/2208
Least Common Multiple of 69,12,96 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 69,12,96 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,12,96) = 3
common factors(in case of two or more numbers have common factors) = 12
GCF(69,12,96) x common factors =3 x 12 = 36
LCM(69,12,96) = ( 69 × 12 × 96 ) / 36
LCM(69,12,96) = 79488 / 36
LCM(69,12,96) = 2208
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FAQs on GCF of Fractions of 829/69, 266/12, 238/96
1. What is the HCF of 829,266,238?
The HCF of 829,266,238 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 829/69, 266/12, 238/96?
Answer: GCF of Numerators as per given numbers 829/69, 266/12, 238/96 is
GCF of Numerators i.e. for 829,266,238 is 1
LCM of denominators i.e. for 69,12,96 is 2208.
Thus, GCF of Fractions is 1/2208.Finally, GCF of Fractions for 829/69, 266/12, 238/96 is 1/2208.